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Cognitively Based Assessment of, for, and as Learning (CBAL) in Mathematics: A Design and First Steps Toward Implementation CBAL ECD

Graf, Edith Aurora; Harris, Karen R.; Marquez, Elizabeth; Fife, James H.; Redman, Margaret
Publication Year:
Report Number:
ETS Research Memorandum
Document Type:
Page Count:
Subject/Key Words:
Mathematics Assessment, Mathematics Cognition, Constructed Response Items, Summative Assessment, Formative Assessment, Mathematics Vocabulary, Cognitively Based Assessment of, for, and as Learning (CBAL), Evidence-Centered Design (ECD)


In this report, we describe the first stages of design and development for the mathematics strand of the Cognitively Based Assessment of, for, and as Learning (CBAL) project. We provide a general rationale for the design as well as a catalog of materials developed so far. The development process for CBAL mathematics represents an application of evidence-centered design (ECD), an approach to assessment formulated by Mislevy and colleagues (e.g., Mislevy, Steinberg, & Almond, 2003). The report is organized into several main sections. The first section provides a brief overview of the literature that motivated the design of a model for mathematical competency. Readers interested in a more in-depth review of the underlying research base may refer to Graf (in press). Subsequent sections describe the evidence model, the task models, and sample tasks. Finally, we discuss how the tasks were assembled into assessments and delivered in a small-scale pilot study. Because the number of tasks and the sample sizes in the pilot study were both very small, we do not draw conclusions about the overall validity of the assessment framework. Instead, we limit our discussion of the pilot results to highlights based on task-specific observations and response patterns that emerged from an exploratory analysis of some of the data.

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